Answer:
500
Step-by-step explanation:
Let's say x represents the number of children's tickets sold, y represents the number of college tickets sold, and z represents the number of adult tickets sold.
For each child ticket sold, we add x to the total. Similarly, for college tickets, we add y and for adult tickets, we add z.
The total revenue can therefore be represented as
(child ticket revenue) + (college ticket revenue) + (adult ticket revenue) =
(price * quantity of children's tickets) + (price * quantity of college tickets) + (price * quantity of adult tickets) =
(1.5 * x) + (3 * y) + (5 * z) = 4950
The total amount of tickets is x+y+z = 1500
The number of college student tickets (y) is 100 less than the number of children's tickets (x), so y = x - 100.
Put these three equations together to get
(1.5 * x) + (3 * y) + (5 * z) = 4950
x+y+z = 1500
y = x-100
Substitute x-100 for y in the second equation
x+(x-100) + z = 1500
add 100 to both sides to isolate the variables
2x + z = 1600
subtract 2x from both sides to isolate the z
1600 - 2x = z
Substitute 1600-2x for z and x-100 for y in the first equation
(1.5 * x) + (3 * y) + (5 * z) = 4950
1.5x + 3*(x-100) + 5 * (1600-2x) = 4950
= 1.5x + 3x - 300 + 8000 - 10x
= 7700 - 5.5x
subtract 7700 from both sides to isolate the x and its coefficient
-2750 = -5.5x
divide both sides by -5.5 to isolate the x
x = 500